Recently, the rapid development of LEO satellite networks spurs another widespread concern-data processing at satellites. However, achieving efficient computation at LEO satellites in highly dynamic satellite networks is challenging and remains an open problem when considering the constrained computation capability of LEO satellites. For the first time, we propose a novel distributed learning framework named SFL-LEO by combining Federated Learning (FL) with Split Learning (SL) to accommodate the high dynamics of LEO satellite networks and the constrained computation capability of LEO satellites by leveraging the periodical orbit traveling feature. The proposed scheme allows training locally by introducing an asynchronous training strategy, i.e., achieving local update when LEO satellites disconnect with the ground station, to provide much more training space and thus increase the training performance. Meanwhile, it aggregates client-side sub-models at the ground station and then distributes them to LEO satellites by borrowing the idea from the federated learning scheme. Experiment results driven by satellite-ground bandwidth measured in Starlink demonstrate that SFL-LEO provides a similar accuracy performance with the conventional SL scheme because it can perform local training even within the disconnection duration.